非黏滞阻尼系统频响函数灵敏度分析的改进计算方法

An improved method for sensitivity analysis of FRF of a system with non-viscous damping

频响函数灵敏度分析是实现频域梯度优化算法的基础。随着各类高阻尼复合材料的广泛应用,黏性阻尼模型假设已不能准确描述其耗能特性。卷积型非黏滞阻尼模型的阻尼力与质点速度的时间历程相关,能够更准确地描述黏弹性材料的阻尼特性。利用复模态叠加法和直接微分法推导出不考虑高阶模态影响的频响函数灵敏度表达式;基于非黏滞阻尼系统矩阵与模态间的关系,提出适用于非黏滞阻尼系统频响函数灵敏度求解的一阶近似法和二阶近似法;通过数值算例验证了提出方法的有效性和准确性。结果表明,与传统方法相比,该改进的计算方法兼顾了计算精度和效率,为实现具有高阻尼性能复合材料结构的动力分析奠定了基础。

Sensitivity analysis of frequency response function(FRF)is the basis of the frequency domain gradient optimization algorithm.With wide application of various kinds high damping composites,the assumption of viscous damping model can’t accurately describe their energy dissipation characteristics.Damping force of the convolution type non-viscous damping model is related to time history of mass point velocity,it can more accurately describe damping characteristics of viscoelastic materials.Here,the sensitivity expression of a system’s FRF without considering effects of higher order modes was derived by using the complex mode superposition method and the direct differential method.Then,based on the relationship between dynamic matrices and modes of a system with non-viscous damping,the first-order approximation method and the second-order approximation method were proposed.Finally,the effectiveness and correctness of the proposed method were verified with numerical examples.The results showed that compared with the traditional method,the proposed method can take into account both calculation accuracy and efficiency to lay a foundation for dynamic analysis of composite structures with high damping performance.